An evaluation of a class of phenomenological theories of ferroelectricity in polycrystalline ceramics

Abstract

Various phenomenological theories of ferroelectricity in polycrystalline ceramics have been proposed in recent years. A particularly attractive class of multiaxial theories with a reduced number of internal variables hinges upon an additive decomposition of the strain and the dipole density into reversible internal variables associated with elasticity and dipole perturbations, and irreversible internal variables associated with dipole switching. It has, however, been recently recognized that these theories can provide unexpected predictions for certain—yet unexceptional—loading histories. The source of the problem was pinned down to the nonconvex dependence of the internal energy on the irreversible variables. The purpose of the present study is to evaluate this more thoroughly. It is found that predictions become unstable above a certain level of mechanical stress, which can be on the order of a few megapascals or even lower for typical sets of material parameters employed in the literature. It is argued that this class of theories should be used with caution, even within their presumed range of validity.